Calculus 1 : Calculus
Study concepts, example questions & explanations for Calculus 1
All Calculus 1 Resources
Example Questions
Example Question #113 : Distance
The velocity of a particle is given by the function 
Velocity is the time derivative of position, and by that token position can be found by integrating a known velocity function with respect to time:
Now, if this integral were to be taken over an interval of time 
For the velocity function
The distance travelled can be found via knowledge of the following derivative properties:
Trigonometric derivative:
The distance travelled over 
Example Question #111 : Distance
Find the distance from points: 
This is simply the application of the distance formula:
The distance 
Example Question #115 : Distance
Determine the distance travelled by a person if their displacement is 
We know that displacement is just the magnitude of the vector moving from point 
Since the person walked 
Example Question #112 : Distance
Determined the displacement of a person who walks 
The displacement in orthogonal directions(North and West) can be determined by using the pythagorean theorem:
Example Question #1 : How To Find Position
Find a vector perpendicular to (4,3).
In general, if we have a vector (a,b), a perpendicular vector is (b,-a).
So here, the perpendicular vector is (3,-4).
Example Question #2 : How To Find Position
if a=i + 2j - 3k and b=4i + 7k, express the vector 3a + 2b.
To express the vector in terms of i, j, and k, we need to combine like terms and distribute.
3a + 2b
= 3(i + 2j - 3k) + 2(4i + 7k)
= 3i + 6j - 9k + 8i + 14k
= 11i +6j + 5k
Example Question #3 : How To Find Position
The velocity of a particle is given by the function 
To find the position from velocity, the function must be integrated. This gives 
Example Question #1 : How To Find Position
The veloctiy of a particle at time 
Cannot be determined.
The position function is the intergral of the velocity function. So here, position is given by 
Example Question #5 : How To Find Position
Find the position at 
To find the position from the acceleration function, integrate the acceleration function twice.
Substitute 
Example Question #6 : How To Find Position
Find the position at 
To find the position function, integrate the acceleration function twice.
Evalute the position at 
Certified Tutor
All Calculus 1 Resources
